399. Evaluate Division，除法求值

题意理解：连乘的问题，链式元素，广度搜索

两个数字看做一条边，每条边有权重;给定两个节点，求出两个节点之间所有链路权重的乘积。

题目剖析：1.先将有向权重关系利用 Map<String,List<Node1,Node2>> 表示出来

 2.利用dfs，遍历所有节点，一直遍历，只有首尾节点符合题目要求的，才符合退出条件，给最终计算结果赋值

题目应用：利用map存储nodeStart和relation的映射关系。利用nodeStart作为链路过程的遍历特征；

    链路过程存入visited，防止死循环
    dfs设定跳出条件，碰到条件即触发退出遍历机制

Equations are given in the format A / B = k, where A and B are variables represented as strings, and k is a real number (floating point number). Given some queries, return the answers. If the answer does not exist, return -1.0.

Example:
Given a / b = 2.0, b / c = 3.0.
queries are: a / c = ?, b / a = ?, a / e = ?, a / a = ?, x / x = ? .
return [6.0, 0.5, -1.0, 1.0, -1.0 ].

The input is: vector<pair<string, string>> equations, vector<double>& values, vector<pair<string, string>> queries , where equations.size() == values.size(), and the values are positive. This represents the equations. Return vector<double>.

According to the example above:

equations = [ ["a", "b"], ["b", "c"] ],
values = [2.0, 3.0],
queries = [ ["a", "c"], ["b", "a"], ["a", "e"], ["a", "a"], ["x", "x"] ]. 

 

The input is always valid. You may assume that evaluating the queries will result in no division by zero and there is no contradiction.

`

package com.jd.jr.nlp;  
  
import java.util.ArrayList;  
import java.util.Arrays;  
import java.util.HashMap;  
import java.util.List;  
  
/\*\*\*  
 \*   将所有的关系 做成 edge-class \*   将所有的关系和 start-node 存入map \*   将所有的关系和 end-node 存入map \* \*   遍历所有queries，递归查找开始和结束的节点 \* \* \*/  
public class Solution399Diy {  
    HashMap<String, List<Edge>> mEdges \= new HashMap<>();  
 double\[\] mRes;  
  
 class Edge{  
        String from;  
  String to;  
 double value;  
 public Edge(String from,String to,double value){  
            this.from\=from;  
 this.to\=to;  
 this.value\=value;  
  
  }  
    }  
  
    public double dfs(String nodeStart,String nodeTo,List<String> visited){  
        if(!mEdges.containsKey(nodeStart)){  
            return \-1.0;  
  }  
        if(!mEdges.containsKey(nodeTo)){  
            return \-1.0;  
  }  
        if(nodeStart.equals(nodeTo)){  
            return 1.0;  
  }  
  
        for(int i=0;i<mEdges.get(nodeStart).size();i++){  
            Edge edge=mEdges.get(nodeStart).get(i);  
 if(visited.contains(edge.to)){  
                continue;  
  }  
            visited.add(nodeStart);  
 double dfsValue=this.dfs(edge.to,nodeTo,visited);  
  
 if(dfsValue==-1.0) {  
//                return -1.0;  
  continue;  
  }else {  
                return edge.value\*dfsValue;  
  }  
        }  
  
        return \-1.0;  
  
  }  
  
    public double\[\] calcEquation(List<List<String>> equations, double\[\] values, List<List<String>> queries) {  
        for(int i=0;i<equations.size();i++){  
            Edge edge1=new Edge(equations.get(i).get(0),equations.get(i).get(1),values\[i\]);  
 if(!mEdges.containsKey(equations.get(i).get(0))){  
                List<Edge> edgeFromList=new ArrayList<>();  
  edgeFromList.add(edge1);  
  mEdges.put(edge1.from,edgeFromList);  
  }else {  
                mEdges.get(equations.get(i).get(0)).add(edge1);  
  }  
  
            Edge edge2=new Edge(equations.get(i).get(1),equations.get(i).get(0),1.0/values\[i\]);  
 if(!mEdges.containsKey(equations.get(i).get(1))){  
                List<Edge> edgeToList=new ArrayList<>();  
  edgeToList.add(edge2);  
  mEdges.put(edge2.from,edgeToList);  
  }else {  
                mEdges.get(equations.get(i).get(1)).add(edge2);  
  }  
        }  
  
        mRes\=new double\[queries.size()\];  
  List<String> visited=new ArrayList<>();  
 for(int i=0;i<queries.size();i++){  
            visited.clear();  
 double vals=this.dfs(queries.get(i).get(0),queries.get(i).get(1),visited);  
  mRes\[i\]=vals;  
  }  
        return mRes;  
  }  
  
  
    public static void main(String\[\] args){  
        Solution399Diy solution399=new Solution399Diy();  
  
//        List<List<String>> equations =new ArrayList<>({"a", "b"},{"b", "c"});  
//        List<List<String>> equations =\[\["a", "b"\],\["b", "c"\]\];  
//        List<String> equations =Arrays.asList("a", "b","b", "c");  
  
//        List<List<String>> equations =new ArrayList<>();  
//        List<String> a1= Arrays.asList("a","b");  
//        List<String> a2=Arrays.asList("b","c");  
//        equations.add(a1);  
//        equations.add(a2);  
////        equations.add(Arrays.asList({"a","b"});  
//  
//        double\[\] values = new double\[2\];  
//        values\[0\]=2.0;  
//        values\[1\]=3.0;  
////        queries = \[ \["a", "c"\], \["b", "a"\], \["a", "e"\], \["a", "a"\], \["x", "x"\] \];  
//        List<List<String>> queries=new ArrayList<>();  
//        List<String> b1=Arrays.asList("a","c");  
//        List<String> b2=Arrays.asList("b","a");  
//        List<String> b3=Arrays.asList("a","e");  
//        List<String> b4=Arrays.asList("a","a");  
//        List<String> b5=Arrays.asList("x","x");  
//        queries.add(b1);  
//        queries.add(b2);  
//        queries.add(b3);  
//        queries.add(b4);  
//        queries.add(b5);  
  
  
  
//        \[\["x1","x2"\],\["x2","x3"\],\["x3","x4"\],\["x4","x5"\]\]  
//\[3.0,4.0,5.0,6.0\]  
//\[\["x1","x5"\],\["x5","x2"\],\["x2","x4"\],\["x2","x2"\],\["x2","x9"\],\["x9","x9"\]\]  
  
  
  List<List<String>> equations =new ArrayList<>();  
  List<String> a1= Arrays.asList("x1","x2");  
  List<String> a2=Arrays.asList("x2","x3");  
  List<String> a3=Arrays.asList("x3","x4");  
  List<String> a4=Arrays.asList("x4","x5");  
  equations.add(a1);  
  equations.add(a2);  
  equations.add(a3);  
  equations.add(a4);  
//        equations.add(Arrays.asList({"a","b"});  
  
  double\[\] values = new double\[4\];  
  values\[0\]=3.0;  
  values\[1\]=4.0;  
  values\[2\]=5.0;  
  values\[3\]=6.0;  
//        queries = \[ \["a", "c"\], \["b", "a"\], \["a", "e"\], \["a", "a"\], \["x", "x"\] \];  
  List<List<String>> queries=new ArrayList<>();  
  List<String> b1=Arrays.asList("x1","x5");  
  List<String> b2=Arrays.asList("x5","x2");  
  List<String> b3=Arrays.asList("x2","x4");  
  List<String> b4=Arrays.asList("x2","x2");  
  List<String> b5=Arrays.asList("x2","x9");  
  List<String> b6=Arrays.asList("x9","x9");  
//        queries.add(b1);  
//        queries.add(b2);  
  queries.add(b3);  
//        queries.add(b4);  
//        queries.add(b5);  
//        queries.add(b6);  
  
  
  Solution399Diy solution3991=new Solution399Diy();  
 double\[\] result=solution3991.calcEquation(equations,values,queries);  
  System.out.println("rersult");  
  System.out.println(result);  
  }  
  
}

`